If we saturate the decay width of the \(P_c\)  with the two-body strong decays to the \(\eta _c N\) , \(\bar{D}^0 \Lambda _c^+\)  and \(J/\psi N\) , we can obtain the total width
\(\Gamma (P_c)=14.32\pm 3.31\,\rm {MeV}\) , which is compatible with the experimental value \(\Gamma _{P_c(4312)} = 9.8\pm 2.7^{+ 3.7}_{- 4.5} \mbox{ MeV}\)  from the LHCb collaboration [1]}.
The present calculations also support assigning the
\(P_c(4312)\)  to be the diquark-diquark-antiquark type hidden-charm pentaquark state with the spin-parity \(J^P={\frac{1}{2}}^-\) . The \(P_c(4312)\)  maybe have a diquark-diquark-antiquark type pentaquark core with the typical size of the \(qqq\) -type baryon states, the strong couplings to the meson-baryon pairs \(\bar{D}^0\Sigma _c^+\)  and \(\bar{D}^-\Sigma _c^{++}\)  lead to some pentaquark molecule components according to the large hadronic coupling constants \(|G_{P\bar{D}^-\Sigma _c^{++}}|= \sqrt{2}|G_{P\bar{D}^0\Sigma _c^+}|\gg |G_{P\bar{D}^0\Lambda _c^+}|\) , and the \(P_c(4312)\)  maybe spend a rather large time as the \(\bar{D}^0\Sigma _c^+\)  and \(\bar{D}^-\Sigma _c^{++}\)  molecular states, just in the case of the \(f_0(980)\) , \(a_0(980)\)  and \(Y(4660)\) . In Ref.[2]}, we assign the \(P_c(4312)\)  to be the \(\bar{D}\Sigma _c\)  pentaquark molecular state with the spin-parity \(J^P={\frac{1}{2}}^-\)  tentatively, and explore its two-body strong decays with the QCD sum rules, and obtain the partial decay widths \(\Gamma \left(P_c(4312)\rightarrow \eta _c N\right)=0.255\,{\rm {MeV}}\)  and \(\Gamma \left(P_c(4312)\rightarrow J/\psi N\right)=9.296\,\,{\rm {MeV}}\) .
The \(P_c(4312)\)  has quite different branching fractions in the scenarios of the pentaquark state and pentaquark molecular state.
We can search for the \(P_c(4312)\)  in the \(\eta _c N\) , \(\bar{D}^0 \Lambda _c^+\)  and \(J/\psi N\)  invariant mass spectrum, and measure the branching fractions
\({\rm Br}\left(P_c(4312)\rightarrow \eta _c N,\, \bar{D}^0 \Lambda _c^+,\, J/\psi N\right)\)  precisely, which maybe shed light on the nature of the \(P_c(4312)\)  unambiguously, test the predictions of the QCD sum rules and examine the hadronic dressing mechanism. If the hadronic dressing mechanism works, the \(P_c(4318)\)  has both the diquark-diquark-antiquark type and meson-baryon type Fock components, we should introduce mixing effects in the interpolating current, and fix the mixing angle by the precise experimental data in the future.
